Digital Electronics: Principles, Devices and Applications

54 Digital ElectronicsCase 2• Let us subtract +24 from +14.• The 2’s complement representation of +14 = 00001110.• The 2’s complement representation of +24 = 00011000.• The 2’s complement of the subtrahend (i.e. +24) = 11101000.• Therefore, +14 − (+24) is given by00001110+ 1110100011110110• The decimal equivalent of (11110110) 2 , which is of course in 2’s complement form, is −10 whichis the correct answer.Case 3• Let us subtract −14 from +24.• The 2’s complement representation of +24 = 00011000 = minuend.• The 2’s complement representation of −14 = 11110010 = subtrahend.• The 2’s complement of the subtrahend (i.e. −14) = 00001110.• Therefore, +24 − (−14) is performed as follows:00011000+ 0000111000100110• The decimal equivalent of (00100110) 2 is +38, which is the correct answer.Case 4• Let us subtract −24 from +14.• The 2’s complement representation of +14 = 00001110 = minuend.• The 2’s complement representation of −24 = 11101000 = subtrahend.• The 2’s complement of the subtrahend (i.e. −24) = 00011000.• Therefore, +14 − (−24) is performed as follows:00001110+ 0001100000100110• The decimal equivalent of (00100110) 2 is +38, which is the correct answer.Case 5• Let us subtract −14 from −24.• The 2’s complement representation of −24 = 11101000 = minuend.